JEE Advance - Mathematics (1989 - No. 27)
Evaluate $$\int {\left( {\sqrt {\tan x} + \sqrt {\cot x} } \right)dx} $$
$$sqrt 2 { an ^{ - 1}}left( {{{sqrt { an x} - sqrt {cot x} } over {sqrt 2 }}}
ight) + C$$
$$sqrt 2 { an ^{ - 1}}left( {{{sqrt { an x} + sqrt {cot x} } over {sqrt 2 }}}
ight) + C$$
$${ an ^{ - 1}}left( {{{sqrt { an x} - sqrt {cot x} } over {sqrt 2 }}}
ight) + C$$
$$sqrt 2 {sin ^{ - 1}}left( {{{sqrt { an x} - sqrt {cot x} } over {sqrt 2 }}}
ight) + C$$
$$sqrt 2 {cos ^{ - 1}}left( {{{sqrt { an x} - sqrt {cot x} } over {sqrt 2 }}}
ight) + C$$